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Model Comparison with Sharpe Ratios

Published online by Cambridge University Press:  09 August 2019

Francisco Barillas ,
Raymond Kan ,
Cesare Robotti  and
Jay Shanken Open the ORCID record for Jay Shanken [Opens in a new window]
Francisco Barillas
Affiliation:
Barillas, [email protected], University of New South Wales School of Banking and Finance
Raymond Kan
Affiliation:
Kan, [email protected], University of Toronto Rotman School of Management
Cesare Robotti
Affiliation:
Robotti, [email protected], University of Warwick Business School
Jay Shanken*
Affiliation:
Shanken, [email protected], Emory University Goizueta Business School and National Bureau of Economic Research (NBER)
*
Shanken (corresponding author), [email protected]
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Abstract

We show how to conduct asymptotically valid tests of model comparison when the extent of model mispricing is gauged by the squared Sharpe ratio improvement measure. This is equivalent to ranking models on their maximum Sharpe ratios, effectively extending the Gibbons, Ross, and Shanken (1989) test to accommodate the comparison of nonnested models. Mimicking portfolios can be substituted for any nontraded model factors, and estimation error in the portfolio weights is taken into account in the statistical inference. A variant of the Fama and French (2018) 6-factor model, with a monthly updated version of the usual value spread, emerges as the dominant model.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 55 , Issue 6 , September 2020 , pp. 1840 - 1874
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2019

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Footnotes

We thank Hendrik Bessembinder (the editor), Wayne Ferson, Seth Pruitt (the referee), Chen Xue, and participants at the 2018 SoFiE Conference, the 2018 Western Finance Association Meetings, the 2018 China International Conference in Finance, the 2018 Institute of Mathematical Statistics (IMS) Asia Pacific Rim Meeting, and the 2017 workshop “New Methods for the Empirical Analysis of Financial Markets” in Comillas, Spain, for helpful comments and suggestions. Finally, we thank Kenneth French for providing us with the data on several factor portfolios used in this article.

References

Asness, C., and Frazzini, A.. “The Devil in HML’s Details.” Journal of Portfolio Management, 39 (2013), 49–68.CrossRefGoogle Scholar
Balduzzi, P., and Robotti, C.. “Mimicking Portfolios, Economic Risk Premia, and Tests of Multi-Beta Models.” Journal of Business and Economic Statistics, 26 (2008), 354–368.CrossRefGoogle Scholar
Ball, R.; Gerakos, J.; Linnainmaa, J. T.; and Nikolaev, V.. “Accruals, Cash Flows, and Operating Profitability in the Cross Section of Stock Returns.” Journal of Financial Economics, 121 (2016), 28–45.CrossRefGoogle Scholar
Barillas, F., and Shanken, J.. “Which Alpha? ” Review of Financial Studies, 30 (2017), 1316–1338.CrossRefGoogle Scholar
Barillas, F., and Shanken, J.. “Comparing Asset Pricing Models.” Journal of Finance, 73 (2018), 715–754.CrossRefGoogle Scholar
Bentler, P. M., and Berkane, M.. “Greatest Lower Bound to the Elliptical Theory Kurtosis Parameter.” Biometrika, 73 (1986), 240–241.CrossRefGoogle Scholar
Breeden, D. T.“An Intertemporal Asset Pricing Model with Stochastic Consumption and Investment Opportunities.” Journal of Financial Economics, 7 (1979), 265–296.CrossRefGoogle Scholar
Carhart, M. M.“On Persistence in Mutual Fund Performance.” Journal of Finance, 52 (1997), 57–82.CrossRefGoogle Scholar
Christie, S.“Is the Sharpe Ratio Useful in Asset Allocation?” Working Paper, Macquarie University (2005).CrossRefGoogle Scholar
Cragg, J. G., and Donald, S. G.. “Inferring the Rank of a Matrix.” Journal of Econometrics, 76 (1997), 223–250.CrossRefGoogle Scholar
Fama, E. F., and French, K. R.. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics, 33 (1993), 3–56.CrossRefGoogle Scholar
Fama, E. F., and French, K. R.. “A Five-Factor Asset Pricing Model.” Journal of Financial Economics, 116 (2015), 1–22.CrossRefGoogle Scholar
Fama, E. F., and French, K. R.. “Choosing Factors.” Journal of Financial Economics, 128 (2018), 234–252.CrossRefGoogle Scholar
Frazzini, A., and Pedersen, L.. “Betting against Beta.” Journal of Financial Economics, 111 (2014), 1–25.CrossRefGoogle Scholar
Gibbons, M. R.; Ross, S. A.; and Shanken, J.. “A Test of the Efficiency of a Given Portfolio.” Econometrica, 57 (1989), 1121–1152.CrossRefGoogle Scholar
Hansen, L. P., and Jagannathan, R.. “Assessing Specification Errors in Stochastic Discount Factor Models.” Journal of Finance, 52 (1997), 557–590.CrossRefGoogle Scholar
Harvey, C.; Liu, Y.; and Zhu, H.. “… and the Cross-Section of Expected Returns.” Review of Financial Studies, 29 (2016), 5–68.CrossRefGoogle Scholar
He, Z.; Kelly, B.; and Manela, A.. “Intermediary Asset Pricing: New Evidence from Many Asset Classes.” Journal of Financial Economics, 126 (2017), 1–35.CrossRefGoogle Scholar
Hou, K.; Xue, C.; and Zhang, L.. “Digesting Anomalies: An Investment Approach.” Review of Financial Studies, 28 (2015), 650–705.CrossRefGoogle Scholar
Huberman, G.; Kandel, S.; and Stambaugh, R. F.. “Mimicking Portfolios and Exact Arbitrage Pricing.” Journal of Finance, 42 (1987), 1–9.CrossRefGoogle Scholar
Jegadeesh, N., and Titman, S.. “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency.” Journal of Finance, 48 (1993), 65–91.CrossRefGoogle Scholar
Jobson, J. D., and Korkie, B. M.. “Estimation of Markowitz Efficient Portfolios.” Journal of the American Statistical Association, 75 (1980), 544–554.CrossRefGoogle Scholar
Jobson, J. D., and Korkie, B. M.. “Performance Hypothesis Testing with the Sharpe and Treynor Measures.” Journal of Finance, 36 (1981), 889–908.CrossRefGoogle Scholar
Jobson, J. D., and Korkie, B. M.. “Potential Performance and Tests of Portfolio Efficiency.” Journal of Financial Economics, 10 (1982), 433–466.CrossRefGoogle Scholar
Kan, R., and Robotti, C.. “Specification Tests of Asset Pricing Models Using Excess Returns.” Journal of Empirical Finance, 15 (2008), 816–838.CrossRefGoogle Scholar
Kan, R.; Robotti, C.; and Shanken, J.. “Pricing Model Performance and the Two-Pass Cross-Sectional Regression Methodology.” Journal of Finance, 68 (2013), 2617–2649.CrossRefGoogle Scholar
Kan, R., and Zhang, C.. “Two-Pass Tests of Asset Pricing Models with Useless Factors.” Journal of Finance, 54 (1999), 203–235.CrossRefGoogle Scholar
Kleibergen, F., and Paap, R.. “Generalized Reduced Rank Tests Using the Singular Value Decomposition.” Journal of Econometrics, 133 (2006), 97–126.CrossRefGoogle Scholar
Lewellen, J. W.; Nagel, S.; and Shanken, J.. “A Skeptical Appraisal of Asset Pricing Tests.” Journal of Financial Economics, 96 (2010), 175–194.CrossRefGoogle Scholar
Lintner, J.“The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” Review of Economics and Statistics, 47 (1965), 13–37.CrossRefGoogle Scholar
Long, J. B.“Stock Prices, Inflation, and the Term Structure of Interest Rates.” Journal of Financial Economics, 1 (1974), 131–170.CrossRefGoogle Scholar
Maller, R. A.; Durand, R. B.; and Jafarpour, H.. “Optimal Portfolio Choice Using the Maximum Sharpe Ratio.” Journal of Risk, 12 (2010), 49–73.CrossRefGoogle Scholar
Maller, R. A.; Roberts, S.; and Tourky, R.. “The Large-Sample Distribution of the Maximum Sharpe Ratio with and without Short Sales.” Journal of Econometrics, 194 (2016), 138–152.CrossRefGoogle Scholar
Maruyama, Y., and Seo, T.. “Estimation of Moment Parameter in Elliptical Distributions.” Journal of the Japan Statistical Society, 33 (2003), 215–229.CrossRefGoogle Scholar
Memmel, C.“Performance Hypothesis Testing with the Sharpe Ratio.” Finance Letters, 1 (2003), 21–23.Google Scholar
Merton, R. C.“An Intertemporal Capital Asset Pricing Model.” Econometrica, 41 (1973), 867–887.CrossRefGoogle Scholar
Newey, W. K., and West, K. D.. “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55 (1987), 703–708.CrossRefGoogle Scholar
Novy-Marx, R.“The Other Side of Value: The Gross Profitability Premium.” Journal of Financial Economics, 108 (2013), 1–28.CrossRefGoogle Scholar
Opdyke, J. D.“Comparing Sharpe Ratios: So Where Are the p-Values? ” Journal of Asset Management, 8 (2007), 308–336.CrossRefGoogle Scholar
Pástor, L., and Stambaugh, R. F.. “Liquidity Risk and Expected Stock Returns.” Journal of Political Economy, 111 (2003), 642–685.CrossRefGoogle Scholar
Robin, J. M., and Smith, R. J.. “Tests of Rank.” Econometric Theory, 16 (2000), 151–175.CrossRefGoogle Scholar
Rubinstein, M.“The Valuation of Uncertain Income Streams and the Pricing of Options.” Bell Journal of Economics, 7 (1976), 407–425.CrossRefGoogle Scholar
Shanken, J.“Intertemporal Asset Pricing: An Empirical Investigation.” Journal of Econometrics, 45 (1990), 99–120.CrossRefGoogle Scholar
Sharpe, W. F.“Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance, 19 (1964), 425–442.Google Scholar
Sharpe, W. F.“Mutual Fund Performance.” Journal of Business, 39 (1966), 119–138.CrossRefGoogle Scholar
Stambaugh, R. F., and Yuan, Y.. “Mispricing Factors.” Review of Financial Studies, 30 (2017), 1270–1315.CrossRefGoogle Scholar
Treynor, J. L., and Black, F.. “How to Use Security Analysis to Improve Portfolio Selection.” Journal of Business, 46 (1973), 66–86.CrossRefGoogle Scholar
Wolak, F. A.“An Exact Test for Multiple Inequality and Equality Constraints in the Linear Regression Model.” Journal of the American Statistical Association, 82 (1987), 782–793.CrossRefGoogle Scholar
Wolak, F. A.“Testing Inequality Constraints in Linear Econometric Models.” Journal of Econometrics, 41 (1989), 205–235.CrossRefGoogle Scholar